Geometry

[Crazy Gamer]

please help me to solve the problem with proper explanation

[Shirsendu Roy]

Area between two intersecting circles given by formula used here as

=(R^2/4)cos^(-1)(1/4)+(R^2)cos^(-1)(7/8)-(R^2/8)(\sqrt{15})

 

area other than inside any of the semicircles and the red shaded part but inside the quarter circle is given as

=(R^2/2)(4-\pi)

area of the semi circle inside the quarter circle is given as (\piR^2)/8

 

Required area= area of the red shaded part=(\piR^2)/4-[(R^2/2)(4-\pi)+(\piR^2)/8+(R^2/4)cos^(-1)(1/4)+(R^2)cos^(-1)(7/8)-(R^2/8)\sqrt{15}] which is the required expression.

 

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